Point Pattern Analysis on a Sphere

Thomas Joseph Lawrence

doi:10.4225/23/5a85314e9cf84

Point Pattern Analysis on a Sphere

Thomas Joseph Lawrence

Research output: Thesis › Master's Thesis

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Abstract

This thesis develops statistical methodology for analysing spatial patterns of points on a sphere. The main results include relevant theory, methods for estimating point process intensity and summary functions such as Ripley's K function, methods for plotting these estimates which have useful properties, and models on the sphere such as the analogue of the Neyman-Scott cluster process. These methods are implemented in code in a software package, and which have been used to analyse the spatial pattern of galaxies. Other possible applications include analysis of initiation points of cyclones, and locations of meteorite impacts, on the Earth's surface.

Original language	English
Qualification	Masters
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Baddeley, Adrian John, Supervisor Nair, Gopalan, Supervisor Milne, Robin, Supervisor
Award date	30 Jan 2018
DOIs	https://doi.org/10.4225/23/5a85314e9cf84
Publication status	Unpublished - 2018

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10.4225/23/5a85314e9cf84

THESIS - MASTER BY RESEARCH - LAWRENCE Thomas Joseph - 2018
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Cite this

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title = "Point Pattern Analysis on a Sphere",

abstract = "This thesis develops statistical methodology for analysing spatial patterns of points on a sphere. The main results include relevant theory, methods for estimating point process intensity and summary functions such as Ripley's K function, methods for plotting these estimates which have useful properties, and models on the sphere such as the analogue of the Neyman-Scott cluster process. These methods are implemented in code in a software package, and which have been used to analyse the spatial pattern of galaxies. Other possible applications include analysis of initiation points of cyclones, and locations of meteorite impacts, on the Earth's surface. ",

keywords = "Nearest-neighbour distance , Point process on sphere, Spherical data, Simulation envelopes, Thomas process, Empty space function, Pair correlation function , Ripley's K function",

author = "Lawrence, {Thomas Joseph}",

year = "2018",

doi = "10.4225/23/5a85314e9cf84",

language = "English",

school = "The University of Western Australia",

}

TY - THES

T1 - Point Pattern Analysis on a Sphere

AU - Lawrence, Thomas Joseph

PY - 2018

Y1 - 2018

N2 - This thesis develops statistical methodology for analysing spatial patterns of points on a sphere. The main results include relevant theory, methods for estimating point process intensity and summary functions such as Ripley's K function, methods for plotting these estimates which have useful properties, and models on the sphere such as the analogue of the Neyman-Scott cluster process. These methods are implemented in code in a software package, and which have been used to analyse the spatial pattern of galaxies. Other possible applications include analysis of initiation points of cyclones, and locations of meteorite impacts, on the Earth's surface.

AB - This thesis develops statistical methodology for analysing spatial patterns of points on a sphere. The main results include relevant theory, methods for estimating point process intensity and summary functions such as Ripley's K function, methods for plotting these estimates which have useful properties, and models on the sphere such as the analogue of the Neyman-Scott cluster process. These methods are implemented in code in a software package, and which have been used to analyse the spatial pattern of galaxies. Other possible applications include analysis of initiation points of cyclones, and locations of meteorite impacts, on the Earth's surface.

KW - Nearest-neighbour distance

KW - Point process on sphere

KW - Spherical data

KW - Simulation envelopes

KW - Thomas process

KW - Empty space function

KW - Pair correlation function

KW - Ripley's K function

U2 - 10.4225/23/5a85314e9cf84

DO - 10.4225/23/5a85314e9cf84

M3 - Master's Thesis

ER -